Thought I was helping to make things easier by using my home email address on computer at library too.I am quite new to computer world with much anxiety .The sharing of an address is making it worse .Any help will be appreciated . 

A bit curious as to why you allowed me to continue only to tell me that you could not help . ? Guess the funny piece is that you asked me not to close a window because it was for feedback . How disappointing that service was . Guess that is my FEEDBACK !

Hi,

Thanks for your question.

Do you mean you've configured the same email account on both computers at home and library? What is the type of account configured in Outlook (POP3, IMAP or Exchange/MAPI)?

"How do I remove address from library BUT keep it on PC at home ?" - If you want to remove this email account from one Outlook client, you can simply go to (take Outlook 2013 as an example here):

FILE>Account Settings>Account Settings...>select the email account that you want to remove>click Remove.

If this is not your case or doesn't help, please elaborate a little bit on your question/symptom, so it will be easy for us to help you.

Regards,

Ethan Hua
TechNet Community Support